M3 MS Jun 2006

Page 1

June 2006 6679 Mechanics M3 Mark Scheme Question Number

Scheme

1.

Use of    y 2 dx  x     xy 2 dx

Marks

 x dx  x   x

2

M1

dx

1 2  1 3   2 x   x   3 x  16 64 x  2 3 8 x 3

Using limits 0 and 4

A1 = A1 M1 A1

(5) [5]

2.

(a)

Small Hemisphere Mass ratios

2 a   3 2

x

3 a 16

3

Bowl

2 7a  3 8

Large Hemisphere 3

2 3 a 3 Anything in the ratio 1 : 7 : 8 3 a 8

x

3 3 a  7  x  8 a 16 8 45 Leading to x a  112 1

(b)

Bowl M

Mass Ratios

45 a 112

x

M

Liquid kM

Bowl and Liquid  k  1 M

3 a 16

17 a 48

45 3 17 a  kM  a   k  1 M  a 112 16 48 2 Leading to k  7

B1

B1

M1 A1 cso

A1

(5)

B1 B1

M1 A1 A1

(5) [10]

1


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